Osio, Elsa; Braicovich, Teresa; Bernardi, Cora; Costes, Cristina About adjoint and \((h,j)\)-adjoint digraphs of \(k\)-regular multigraphs. (Sobre digrafos adjuntos y \((h,j)\) adjuntos de multidigrafos \(k\)-regulares.) (Spanish. English summary) Zbl 1099.05507 Rev. Colomb. Mat. 37, No. 2, 81-86 (2003). Summary: This work connects graph theory with matrix theory. We prove that every \({}^{(h,j)}G\) digraph of a \(k\)-regular multidigraph on \(n\) vertices has exactly \([k^{(h-j)}!]^{n\cdot k^j}\) different covering \((k^{(h-j)}-1)\)-regular subdigraphs. The proof is via a suitable matrix representation, using the permanent of the precedence matrix of the \((h,j)\)-adjoint digraphs. MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:adjunction; precedence matrix; matrix representation PDFBibTeX XMLCite \textit{E. Osio} et al., Rev. Colomb. Mat. 37, No. 2, 81--86 (2003; Zbl 1099.05507) Full Text: EuDML